Problem: There are five unmarked envelopes on a table, each with a letter for a different person.  If the mail is randomly distributed to these five people, with each person getting one letter, what is the probability that exactly four people get the right letter?
Answer: If 4 people get the right letter, then there is only one letter left, and only one person left.  So, the last person will get the right letter, too.  Therefore, it is impossible for exactly four people to get the right letter.  So, the probability is $\boxed{0}$.